The methods, systems and halftone screen sets illustrated herein in embodiments are related generally to the art of halftoning images. More specifically, embodiments are related to methods for selecting sets of halftone screens that do not generate objectionable moiré when interacting with a problematic excitation associated with a rendering device or an image. Embodiments disclosed herein include image processors that include such screens and are adapted to apply them. Additionally, specific screen sets for avoiding objectionable moiré when combined with specific problematic excitations are disclosed. Embodiments will be described with reference to marking engines or printers. However, embodiments will find application in other imaging systems that use halftoning to render an image.
Digital imaging systems, including, for example, ink jet, electrophotographic and xerographic printing or rendering environments can include a number of intentional and unintentional periodicities in their rendering processes. For example, many raster output scanners associated with electrophotographic and xerographic marking engines include a rotating polygonal mirror. One or more laser beams are reflected off of facets of the rotating mirror onto an imaging surface. Imperfections in the mirrors, the mirrors' alignment, and the rate at which the mirror is rotated can affect the position and focus of the reflected beam with the periodicity of the mirror rotation. The cyclic nature of gears associated, for example, with moving an ink jet print head or with transporting print media, also contributes periodicities to the rendering process. Additionally, where print media is transported by or processed by rolls, roll run-out or imperfections in the shape or alignment of the rolls can contribute periodic variations in the rendering process. For instance, roll run-out imperfections may create variation to development pressure and/or in-media transportation speed. Furthermore, subtle accelerations and decelerations are associated with points in time of positive gear-tooth engagement and disengagement (or backlash).
In the best of situations, these periodic excitations occur at frequencies that are high enough to be imperceptible by the human vision system. However, even excitations that are themselves at an imperceptively high frequency can combine or beat with other imaging excitations to produce perceptible banding or moiré artifacts in a rendered image. For example, problematic rendering excitations can combine with fundamental, harmonic and beat frequencies associated with halftone screens used in the rendering process.
In monochrome or black and white rendering applications, wherein only one halftone screen is used, it is fairly simple to select a halftone screen that does not include excitations (i.e., fundamental, harmonic and beat frequencies) in the same direction or at the same angle as one or more known problematic excitations. However, in color rendering, wherein two or more halftone screens are used (one for each separation), it is difficult to find a set of halftone screens that avoid including excitations (i.e., fundamentals, harmonics and beats) that avoid the direction or angle of a problematic excitation.
Indeed, a great deal of effort has been spent to solve the lesser problem of finding sets of halftone screens for rendering color that do not produce objectionable moiré due to beats between frequency components of the screens themselves. For example, see Spectral Analysis and Minimization of Moiré Patterns in Color Separation by Amidror, Hersch and Ostromoukhov in the Journal of Electronic Imaging, Vol. 3, no. 3, pages 295-317 (July 1994). U.S. Pat. No. 5,381,247 to Hains for a Method for Reducing Two-Color Moiré in Four-Color printing, which issued Jan. 10, 1995; U.S. Pat. No. 4,537,470 to Schoppmeyer for Screen Systems for Multicolor Printing, which issued Aug. 27, 1985; U.S. Pat. No. 5,381,247 to Hains for a Method for Reducing Two-Color Moiré in Four-Color Printing, which issued Jan. 10, 1995; and U.S. Pat. No. 6,798,539 B1 to Wang, et al. for a method for moiré-free color halftoning using non-orthogonal cluster screens, which issued Sep. 28, 2004.
Therefore, there has been a desire for methods for selecting sets of halftone screens for rendering separations of a color image that avoid excitations in directions near a direction of a problematic excitation, for screens that meet that criteria, and for imaging systems that render images through the use of halftone screens that meet that criteria.